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Math Help - Inflection Points question

  1. #1
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    Inflection Points question

    f(x)=-8x^4-5x^3 +3 for concavity and inflection points.

    f(x)=-8x^4-5x^3 +3
    f'(x)=-32x^3-15x^2
    f''(x)=-96x^2-30x

    can someone explain to me what exactly Inflection Points are?
    is it like critical points for the first derivative but those are for the second one?
    i mean, making f''(x) = 0 and get 2 numbers and those are the Inflection Points?
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  2. #2
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    Quote Originally Posted by Baatata View Post
    f(x)=-8x^4-5x^3 +3 for concavity and inflection points.

    f(x)=-8x^4-5x^3 +3
    f'(x)=-32x^3-15x^2
    f''(x)=-96x^2-30x

    can someone explain to me what exactly Inflection Points are?
    is it like critical points for the first derivative but those are for the second one?
    i mean, making f''(x) = 0 and get 2 numbers and those are the Inflection Points?

    inflection points are when the original function changes concavity.
    so, yes, set the second derivative equal to 0, and see where the changes occur
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  3. #3
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    Quote Originally Posted by twostep08 View Post
    inflection points are when the original function changes concavity.
    so, yes, set the second derivative equal to 0, and see where the changes occur
    okay so i get x=0 and 10/32
    is this right?

    now i have to plug it in f(x) and those are my 2 values? (if yes then i get 3 and 2.923 is this right?)
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